Average Error: 0.0 → 0.0
Time: 39.2s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
↓
\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r65738 = x;
        double r65739 = y;
        double r65740 = 1.0;
        double r65741 = r65739 - r65740;
        double r65742 = z;
        double r65743 = r65741 * r65742;
        double r65744 = r65738 - r65743;
        double r65745 = t;
        double r65746 = r65745 - r65740;
        double r65747 = a;
        double r65748 = r65746 * r65747;
        double r65749 = r65744 - r65748;
        double r65750 = r65739 + r65745;
        double r65751 = 2.0;
        double r65752 = r65750 - r65751;
        double r65753 = b;
        double r65754 = r65752 * r65753;
        double r65755 = r65749 + r65754;
        return r65755;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r65756 = b;
        double r65757 = y;
        double r65758 = t;
        double r65759 = r65757 + r65758;
        double r65760 = 2.0;
        double r65761 = r65759 - r65760;
        double r65762 = z;
        double r65763 = 1.0;
        double r65764 = r65763 - r65757;
        double r65765 = a;
        double r65766 = r65763 - r65758;
        double r65767 = x;
        double r65768 = fma(r65765, r65766, r65767);
        double r65769 = fma(r65762, r65764, r65768);
        double r65770 = fma(r65756, r65761, r65769);
        return r65770;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 0.0

    \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) b)))